Some results about the behaviour of the characteristic frequencies in electric circuits

In this work calculations of characteristic modes in electric circuits are shown by using the Lagrangian formulation. The effects of changing the values of the elements of the circuit upon the characteristic modes, are also studied. Also, the results point out that the effect of removing a branch in the circuit, determine as a consequence, that the new characteristic modes are inserted among the old ones. In summary, we can obtain as a first approximation some information about the behaviour of the characteristic frequencies of circuits subjected to changing conditions or imposed constraints, by linearization of their equivalent Lagrangian system in the neighborhood of an equilibrium state, and by applying to the latter some results deriving from the Rayleigh-Courant-Fisher theorem for systems performing small oscillations